A body of mass 1 kg falls freely from a height of 100 m on a platform of mass 3 kg which is mounted on a spring having spring constant k = 1.25 × 10⁶ N/m. The body sticks to the platform and the spring’s maximum compression is found to be x. Given that g = 10 ms^–2, the value of x will be close to $\_\_\_\_\_\_$ cm

The body will momentarily come to rest when the spring has fully compressed, which will happen at that point.
In other words, the spring will receive the entire energy gain from falling.

Energy gained after a height fall,

$\mathrm{h}=(100+\mathrm{x}) \mathrm{meter} \mathrm{is} \mathrm{mgh}=\mathrm{mg}(100+\mathrm{x})$

This entire thing is given to the spring.
The spring's energy gain is 

$\frac{1}{2}{\mathrm{kx}}^2=0.625\times {10}^6{\mathrm{x}}^2=1\times 10(100+\mathrm{x})$

$\mathrm{x}=0.4=4\mathrm{cm}$

Hence the correct answer is 4.